Nuprl Lemma : seteqtrans_wf
seteqtrans() ∈ ∀s1,s2,s3:coSet{i:l}. (seteq(s1;s2) ⇒ seteq(s2;s3) ⇒ seteq(s1;s3))
Proof
Definitions occuring in Statement :
seteqtrans: seteqtrans(),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
seteqtrans1_ext,
seteqtrans: seteqtrans()
Lemmas referenced :
seteqtrans1_ext
Rules used in proof :
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalRule,
sqequalSubstitution
Latex:
seteqtrans() \mmember{} \mforall{}s1,s2,s3:coSet\{i:l\}. (seteq(s1;s2) {}\mRightarrow{} seteq(s2;s3) {}\mRightarrow{} seteq(s1;s3))
Date html generated:
2018_07_29-AM-09_51_19
Last ObjectModification:
2018_07_11-PM-00_16_21
Theory : constructive!set!theory
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